Representações matriciais dos conceitos de estabilidade Berge no modelo de grafos para resolução de conflitos - Cordeiro, Yan Saraiva (2021)
Conflicts occur in virtually all sectors of society. In game theory, potential resolutions to a conflict are found through stability analysis, based on stability definitions with precise mathematical structures. The Graph Model for Conflict Resolution (GMCR) provides an efficient way to model and analyze a strategic conflict. The GMCR can model reactions and counter-reactions following different stability definitions that seek to represent human behavior in conflict situations. Berge stabilities, for example, are useful for analyzing interactions between decision makers with altruistic behaviors, that is, in strategic situations where DMs act to improve the well-being of other DM(s). An effective and convenient way of calculating and coding stability analyzes is to use matrix systems to represent stability concepts. This work aimed to develop matrix expressions to determine the Berge stabilities of states in the GMCR for bilateral and multilateral conflicts. To illustrate the applicability of this matrix representation, two classic conflicts of the literature were analyzed. For the bilateral case, the conflict of values was analyzed and, for the multilateral case, the Elmira conflict was analyzed.